Suspended-sediment rating curve response to urbanization and

wildfire, Santa Ana River, California

Jonathan A. Warrick1 and David M. Rubin1

Received 15 August 2006; revised 6 December 2006; accepted 22 January 2007; published 18 May 2007.

[1] River suspended-sediment concentrations provide insights to the erosion and transportof materials from a landscape, and changes in concentrations with time may result fromlandscape processes or human disturbance. Here we show that suspended-sedimentconcentrations in the Santa Ana River, California, decreased 20-fold with respect todischarge during a 34-year period (1968�2001). These decreases cannot be attributed tochanges in sampling technique or timing, nor to event or seasonal hysteresis. Annual peakand total discharge, however, reveal sixfold increases over the 34-year record, whichlargely explain the decreases in sediment concentration by a nonlinear dilution process.The hydrological changes were related to the widespread urbanization of the watershed,which resulted in increases in storm water discharge without detectable alteration ofsediment discharge, thus reducing suspended-sediment concentrations. Periodic uplandwildfire significantly increased water discharge, sediment discharge, and suspended-sediment concentrations and thus further altered the rating curve with time. Our resultssuggest that previous inventories of southern California sediment flux, which assumetime-constant rating curves and extend these curves beyond the sampling history,may have substantially overestimated loads during the most recent decades.

Citation: Warrick, J. A., and D. M. Rubin (2007), Suspended-sediment rating curve response to urbanization and wildfire, Santa Ana

River, California, J. Geophys. Res., 112, F02018, doi:10.1029/2006JF000662.

1. Introduction

[2] Sediment flux measurements from rivers are impor-tant for evaluating terrestrial organic and inorganic materialexport, landscape denudation, geomorphic change, habitatand water quality, and inputs to reservoir and coastalsystems. Rates of sediment discharge are related to thesources, transport and storage of sediment within a water-shed, which are in turn related to tectonic regime, climate,land cover, land use, and river setting [Milliman andSyvitski, 1992; Dinehart, 1998; Trimble, 1997, 1999;Burbank and Anderson, 2001; Yang et al., 2005]. Globalinventories of river discharge suggest that both acceleratedrates of soil erosion and trapping of sediment by dams havealtered these fluxes during recent decades [Walling andFang, 2003; Syvitski et al., 2005].[3] The finest fraction, and commonly the majority, of

river sediment flux is transported below theoretical transportcapacities, which necessitates the development of site-specific, empirical relationships to compute flux [Colby,1963; Porterfield, 1972; Walling, 1977]. These empiricalrelationships between river discharge and suspended-sedimentconcentration respond to patterns of sediment production,availability and transport capacity throughout a watershed,which may include sediment-production variability of rivertributaries [Meade et al., 1990; Hicks et al., 2000; Lenzi and

Marchi, 2000], changes in bed sediment grain size [Rubinand Topping, 2001], flow rate dynamics and event hyster-esis [Walling, 1974; Williams, 1989; Rubin and Topping,2001], and seasonal to interannual changes in sedimentsupply [Leopold, 1968; Walling, 1974; Van Sickle andBeschta, 1983; Dinehart, 1998; Asselman, 2000; Toppinget al., 2000]. Thus simple sediment rating curve relation-ships (e.g., power law) may not adequately reproduce thevariability in sediment production, and hence flux, owing tononlinear or time-dependent effects [e.g., Van Sickle andBeschta, 1983; Hicks et al., 2000; Hovius et al., 2000;Horowitz, 2003]. Further, a comprehensive analysis ofNorth American suspended-sediment rating curves suggeststhat water discharge also plays a controlling factor in thecurve variability [Syvitski et al., 2000], although little workhas examined the effects of hydrologic change on ratingcurves.[4] The rivers of southern California drain a semiarid

landscape that has been subject to periodic wildfire, exten-sive population and urban growth, and channel modifica-tions including large dams [Brownlie and Taylor, 1981;Inman and Jenkins, 1999; Lave and Burbank, 2004]. Theserivers are also recognized to be highly event-driven,producing the majority of long-term discharge and sedimentflux during brief, intense winter events [Kroll, 1975;Warrick and Milliman, 2003]. Thus, owing to their smallsize, high relief, active tectonics, and history of humandevelopment, southern California rivers serve as examplesof high-sediment-yield, small, mountainous rivers withconsiderable human modification [Milliman and Syvitski,

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1U.S. Geological Survey, Santa Cruz, California, USA.

This paper is not subject to U.S. copyright.Published in 2007 by the American Geophysical Union.

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1992]. The Santa Ana River is unique for southern Cal-ifornia in that through a multidecadal period of land usechange and multiple wildfires, the U.S. Geological Survey(USGS) continued stream gauging and event-based sus-pended-sediment sampling operations at a station near theriver mouth. These data prove to be exceptionally valuable,because they clearly reveal that order-of-magnitude changesin suspended-sediment concentrations occurred over thethree-decade sampling period. We show here that thesechanges were largely caused by altered rates of waterdischarge, rather than the more commonly cited sedimentsupply modifications discussed above. Trends and variabilityin discharge rates were strongly correlated with the landscapechanges in urbanization and wildfire.

2. Santa Ana River

[5] The Santa Ana River drains a 4406 km2 basin thatincludes the San Gabriel and San Bernardino Mountains(maximum relief = 3500 m) and a large flood controlstructure, Prado Dam (Figure 1). Built in 1941, PradoDam traps discharge from 3859 km2 (or 87.6%) of thewatershed, with the primary purpose of regulation of winterstormflow for downstream flood control and groundwaterrecharge in Orange County Water District (OCWD) perco-lation basins [U.S. Army Corps of Engineers, 1994]. Thusthe ‘‘upper watershed’’ (above Prado Dam) drains the steepinland mountains and a flat inland plain, while the ‘‘lowerwatershed’’ (below Prado Dam) drains the lower lying SantaAna Mountains (maximum relief = 1730 m) and a portionof the coastal plain of Orange County (Figure 1).[6] The Santa Ana River has urbanized rapidly since the

mid-20th century, and the location of this development haslargely occurred in lowlands that were previously used foragriculture (Figure 1) [California Department of WaterResources, 1960] (also California Department of Conserva-tion (CADC) Farmland Mapping and Monitoring Pro-gram—Standard and custom map products, http://www.consrv.ca.gov/DLRP/fmmp/map_products/index.htm,

accessed 11 August 2003) (hereinafter referred to as CADConline data). By 2000, approximately 40% of the basin hadbeen developed into urban land uses, a rate consistent inboth the upper and lower basins and coincidental with rapidpopulation increases (Figure 2).[7] Water and sediment discharge in the Santa Ana River

is dominated by brief runoff events during wet winterstorms occurring mostly in December�March. On average,half of the annual discharge and �90% of the sediment fluxto the ocean occurs during just 3 days per year, while theriver discharges nothing to the ocean during �70% of thetime [Kroll, 1975; Warrick and Milliman, 2003]. Thesedischarge patterns are similar to the event-based dischargepatterns of unregulated rivers of southern California due toPrado Dam operations: The majority of upper basin water iscaptured by Prado Dam and diverted to groundwaterrecharge facilities immediately downstream of the dam[U.S. Army Corps of Engineers, 1994]. Some upper water-shed discharge is released to the river mouth during storms,however, as reservoir storage is drained during or soon afterfloods to provide for maximum reservoir storage and todrain riparian habitats behind the dam [Izbicki et al., 1998].Owing to the high variability of annual precipitation,discharge in the Santa Ana River can vary by manyorders-of-magnitude from year to year and can be excep-

Figure 1. Santa Ana River watershed, including urbanizedareas in 1957 and 2000 (see Figure 2 for data sources),Prado Dam, USGS gauging stations, and NWS rain gauge atSanta Ana (ANA).

Figure 2. Urban land-use and population data for theSanta Ana River watershed region. USGS sampling(1968�2001) shown with gray shading. (a) Urban landuse for both the upper and lower basins of the Santa AnaRiver after California Department of Water Resources(CADWR) [1960], CADC (online data), and unpublishedCADWR data (provided by G. I. Bergquist, personalcommunication, 2003). (b) Total population of the threecounties of the watershed from U.S. Census Bureau [2003].SBC, San Bernardino County; RC, Riverside County; OC,Orange County. Portions of each county population liveoutside of the watershed.

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tionally high during El Nino�Southern Oscillation (ENSO)winters [Inman and Jenkins, 1999; Warrick and Milliman,2003; Andrews et al., 2004].

3. Suspended-Sediment Rating Curve

[8] The relationship between instantaneous discharge andsuspended-sediment concentration at the last USGS stationon the Santa Ana River (USGS 11078000; Figure 1) revealsa positive, yet somewhat weak relationship between dis-charge and concentration (Figure 3). Scatter about a powerlaw regression relationship through these data is high (r2 =0.53), and the high error of this relationship (r.m.s.e. =0.54 log10 units) represents over an order-of-magnitudespread about the fitted relationship. The large r.m.s. errorcannot be attributed to changes in the sampling technique orsampling timing with respect to the event or annual hydro-graph (Appendix A). Sampling has consistently focused ondays of peak event discharge throughout the samplingrecord, and 77% of all samples have been taken within1 day of peak discharge (Appendix A).[9] Sample date, on the other hand, explains roughly half

of the variability associated with the original power lawrelationship residuals (r2 = 0.48; Figure 4). A fitted expo-nential function suggests that the residuals decreased by anaverage of 1.3 log10 units, or �20-fold, between 1968 and2001 (Figure 4). Further, mean residuals for each water yearreveal that this drop occurred somewhat gradually over timerather than abruptly (Figure 4b). This time-dependency ofthe Santa Ana River rating curve can be shown to besignificant with other analyses. For example, the combina-tion of discharge and date of sample in multiple-variableregression reveals that both variables are highly significant(p < 0.01) producing an improved correlation coefficient(r2) of 0.75 and r.m.s. error of 0.40 log10 units.

[10] The combined analyses above assume that concen-tration changes were consistent across the range ofmeasured discharge rates. To test this, we conducted twotime-dependent, nonlinear regressions, the first of whichboth power law slope (b) and offset (a) were allowed tochange with time according to

Css ¼ a tð ÞQb tð Þ;such that a tð Þ ¼ ai e

�mat;b tð Þ ¼ mb t þ bi;

ð1Þ

where t is time in days since 10/1/1967, ai and bi are theinitial values at ti = 0, and ma and mb are the rates of changewith time. Results of this analysis are shown with a series ofthin lines in Figure 3, and both a and b were significantlyrelated to time (p < 0.01 and p < 0.05, respectively). Thisnonlinear, time-dependent relationship explained only 1%more variance in the concentrations (r2 = 0.76, r.m.s.e. = 0.39;Figure 3) than the linear relationships discussed above.Secondly, we conducted moving-window power lawregressions through the data and allowed the regressionsample window to vary between 5 and 100 samples.Complete significance (all regression p < 0.05) occurred forsample windows of 21 to 100 samples. Highly significant(p < 0.01) time-dependence was shown for both the powerlaw offset (a) and slope (b) across the complete record, andtotal offsets were �1.2 (±0.1) and 0.17 (±0.05), respec-tively, for the range of window lengths. Values of a and bdid not change abruptly with time.[11] Hence all analyses suggest that concentration

changes on the order of 20-fold have occurred across thebroad range of sampled discharge rates. Although a slightincrease in power law slope was found with time (e.g.,Figure 3), this change explains little of the variance in theconcentration data. The main change in the rating curve is agradual downward shift with time. There is thus a highlysignificant, decadal-scale time-dependency in the suspendedsediment concentrations for the lower Santa Ana River.Below we examine hydrologic variables from the USGSgauging station to evaluate the source(s) of this time-dependent relationship.

4. Analysis of Hydrologic Change

[12] Four variables from the Santa Ana River wereevaluated for change with respect to time: precipitation,annual peak discharge, annual water discharge, and annualsediment discharge. Four precipitation stations near orwithin the Santa Ana River watershed were found to spanthe 1968�2001 record, a monthly recording NationalWeather Service precipitation gauge at the Santa Ana FireStation (ANA in Figure 1; http://cdec.water.ca.gov/) andthree daily recording stations in the U.S. HistoricalClimatology Network (049087-Tustin Irvine Ranch,047306-Redlands and 046719-Pasadena [Williams et al.,2004]). The ANA data were shown to correlate best withthe Santa Ana River discharge data, as discussed below, andare generally used in our analyses.[13] Discharge variables for the water years sampled

(1968�2001) were obtained from the USGS Surface WaterDatabase (http://waterdata.usgs.gov/nwis/sw) for stations11078000 (Santa Ana River at Santa Ana) and 11074000

Figure 3. Suspended-sediment concentration measure-ments from the Santa Ana River at Santa Ana (USGS11078000). Symbols are shaded according to sample date(see inset). Data have been fit by a power law (thick dashedline, r2 = 0.53) and a nonlinear, time-dependent function(series of black lines; r2 = 0.76; see text for methods).

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(Santa Ana River below Prado Dam). The USGS alsoestimated and published daily suspended-sediment fluxrates for the Santa Ana River during water years 1968–1985 using the techniques of Porterfield [1972] (dataavailable at: http://co.water.usgs.gov/sediment/). We usedthese 19 years of USGS sediment discharge estimates tocompare with our sediment flux computations for the entire34-year record.[14] Suspended-sediment discharge (Qss in t/d) was com-

puted as the product of average daily water discharge data(Q in m3/sec) and time-dependent discharge-suspended-sediment concentration (Css) relationships,

Qss ¼ Q tð ÞCss tð Þ: ð2Þ

Because sediment concentrations were not related to eventor seasonal hysteresis (Appendix A), sophisticated techni-ques for including sediment supply limitations were notemployed [e.g., Van Sickle and Beschta, 1983]. Rather, weevaluated the decadal-scale changes with three differentrating curves. These rating curves included: (1) the powerlaw fit corrected for the exponential, time-dependentresidual decrease (Figure 4a),

Css ¼ 841:3Q0:65exp �0:0002446tð Þ; ð3Þ

where Css, Q, and t have units of mg/l, m3/s, and days since1 October 1967, respectively; (2) the power law (Figure 3)corrected with individual water year mean concentrationresiduals n > 4 (Figure 4b) or the trend in residuals whenn < 4; and (3) the best-fit nonlinear rating curve usingequation (1) (thin lines, Figure 3). Concentration estimateswere corrected for logarithmic-transformation biases usingdaily corrections suggested by Hicks et al. [2000], becausethe rating curve errors were discharge dependent (Figure 5).Bias correction resulted in total mass discharge increases ofonly 4�5% for the three rating curves techniques.[15] Comparison of the rating-curve results and USGS

estimates of sediment flux during 1968�1985 are shown inFigure 6. There is general agreement between the methodsover the many orders-of-magnitude of annual sedimentdischarge, and r.m.s. differences are 0.22 to 0.26 log10 unitsfor each method. The rating-curve techniques, however,generally underpredict USGS estimates at the lowest fluxes(<100 kt/yr; Figure 6), and there is a mean systematic biasfor each method of �0.16 to �0.19 log10 units. There is notime-dependence (p < 0.05), however, in the biases of anyof the rating curve methods, which suggests that both therating curve and USGS techniques are consistent in includ-ing the time-dependent sediment concentration relationshipsdiscussed above. For the results presented below, we choseto present results from rating curve method 2: annualoffsets, because (1) it resulted in low log10 r.m.s. errorsand biases and the lowest linear r.m.s. errors and biases withrespect to the USGS results, (2) it includes annual variabil-ity in concentrations (Figure 4b) that may be related toactual sediment source variability, and (3) it does notinclude the potential, or apparent, biases of the flexibleUSGS methodologies detailed by Porterfield [1972]. Wenote, however, that although the three rating-curve techni-ques produce slightly different estimates of flux, they allproduce the same statistical relationships and conclusionspresented below.

Figure 4. Suspended-sediment concentration residuals forthe Santa Ana River at Santa Ana (USGS 11078000).Residuals are calculated as the difference between measuredconcentration and the calculated concentration from thebest-fit power law rating curve relationship (dashed line inFigure 3). Solid lines are best-fit exponential relationships(p < 0.01).

Figure 5. Running local mean standard error of the residualsbetween measured suspended-sediment concentration and thetime-dependent rating curve.

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[16] Time series of the four hydrologic variables over theperiod of suspended-sediment sampling (1968�2001) areshown in Figure 7. There is both substantial year-to-yearvariability in the data and multiyear periods of high andlow precipitation and discharge. For example, two well-recognized multiyear periods of low precipitation anddischarge occur during 1970�1977 and 1984�1991 [cf.Inman and Jenkins, 1999] (Figure 7).[17] To evaluate time-dependence in discharge we used

precipitation as a dependent variable in a series of statisticaltests [cf. Alley, 1988]. Owing to the semiarid climate ofsouthern California, winter precipitation clearly provides theprimary condition for river discharge variability [cf.Brownlieand Taylor, 1981]. Others researchers [see, e.g., Lave andBurbank, 2004] have noted that precipitation intensity ratherthan total annual precipitation better explains water andsediment discharge rates, such that precipitation index (PI),

PI ¼ SPAt ; ð4Þ

better correlates with discharge measurements, where Pt is at-hour precipitation intensity, A is a fitted coefficienttypically >1, and Pt

A are summed over a hydrologic yearor storm series. We utilized equation (4) with data fromthree USHCN daily precipitation stations in close proximityof the watershed (stations 049087, 047306, and 046719)and found that annual PI correlated significantly (p < 0.05)with annual water and sediment discharge measurementsunder the conditions 1 < A < 3.6. However, peak correlationfor all analyses occurred for A values of 1.0 to 1.4, andnegligible benefit was exhibited for A > 1 (maximum r2

improvement for A 6¼ 1 was 0.006). Thus we present all

results below with respect to annual precipitation values(i.e., A = 1).[18] Positive relationships are exhibited between annual

precipitation and all discharge measurements (Figures 8a–8c). Residuals about these relationships reveal that bothannual and peak water discharge are significantly correlatedwith time, while sediment discharge was not significantlycorrelated with time (Figures 8d–8f). The rates of increasesuggest a 280% (±170%) increase in total annual waterdischarge and a 350% (±150%) increase in peak dischargewith respect to precipitation over the 34-year record. Of allof the years in the record, 1969 is clearly unique: Not onlydoes it have high water and sediment discharge (accountingfor approximately half of the total 1968�2001 sedimentflux; Figure 7), but also the water- and sediment-discharge

Figure 7. Hydrologic data for the Santa Ana River atSanta Ana (USGS 11078000) during the period ofsuspended-sediment measurements. Thick line is the 10-yearrunning median value, and dashed lines are 10-year running20 and 80 percentile values. (a) Annual precipitation at NWSSanta Ana station (ANA). (b) Annual peak discharge.(c) Total annual discharge. (d) Annual suspended-sedimentdischarge.

Figure 6. Comparison of USGS suspended-sediment fluxcomputations with flux results from three time-dependentsediment rating curves: exponential decrease in offset(triangles), annual concentration residuals (squares), andnonlinear time dependence (circles).

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residuals were unusually large with respect to the generaltrends in the remaining data (Figures 8d–8f). Below we showevidence that these anomalously high fluxes are related to alarge wildfire.[19] We then evaluated whether scale-dependent temporal

changes existed in the data using the time-dependent,nonlinear model found in equation (1). For these analyses,Css was replaced with the three hydrologic variables and Qwas replaced with annual precipitation. Results suggest thatall variables reveal some scale dependence in the temporalchanges, and all b and a are highly significant with respectto time (p < 0.01; Figure 9). Both annual discharge and peakdischarge show order-of-magnitude increases duringthe driest years, while having negligible temporal changeduring the wettest years (Figures 9a and 9b). Althoughsuspended-sediment flux did not show significant temporalchanges in the scale-independent results presented previ-ously (Figure 8f), the scale-dependent analyses suggest thatdecreases were exhibited for the high-rainfall years(Figure 9c).[20] Summarizing, although linear models significantly

fit the time-dependent changes for total and peak discharge(Figure 8), we note that highly significant, scale-dependentand nonlinear changes are exhibited in all data (Figure 9).These changes are not in the same direction with respect toprecipitation, however, water discharge increased throughtime whereas sediment discharge decreased. Below weshow that these changes are strongly correlated with thewildfire and urbanization history of the basin.

5. Sources of Change

[21] Results presented above suggest that significantchanges occurred in suspended-sediment concentrations,

water discharge and sediment flux. Below we examine theprocesses that may have caused these changes beforeintegrating these findings into a suspended-sediment con-ceptual model for the Santa Ana River.

5.1. Upper Watershed

[22] The upper watershed of the Santa Ana River(Figure 1) cannot be overlooked as a potential source ofthe change exhibited. Discharge through Prado Dam cap-tures these upper watershed inputs, and USGS gauging andsampling records at 11074000 (Figure 1) capture the time-history of discharge at this site. Peak discharge recordsbelow Prado Dam reveal increases in peak discharge withtime that are similar in magnitude to the lower watershedgauge (data not shown). However, these rates of peakdischarge were consistently twofold to fourfold lower thanthose measured at the river mouth (Figure 10). This sug-gests that although rates of upper basin water dischargeincreased with time, they do not represent the majority ofdischarge during event peaks, when suspended sedimentsampling has dominantly been conducted (Appendix A).[23] The influence of upper basin sediment fluxes on the

suspended-sediment results was evaluated with a sedimentmass balance. For this mass balance we examined: sedi-mentation behind Prado Dam, sediment discharge immedi-ately downstream of Prado Dam, and lower basincontributions of sediment (Figure 11). Total sedimentationbehind Prado Dam was estimated from U.S. Army Corps ofEngineers surveys of the reservoir conducted during 1960,1975 and 1988, which suggest that sedimentation has been0.927 million m3/yr since dam construction, although thisrate fluctuated (0.389–1.567 million m3/yr) between thethree surveys [U.S. Army Corps of Engineers, 2003] (alsoGreg Peacock, USACE, personal communication, 2004).

Figure 8. Relationship between annual precipitation and (a) total annual discharge, (b) annual peakdischarge, and (c) suspended-sediment discharge for USGS 11078000. Best-fit power law relationships(solid lines) and correlation coefficients are shown. (d, e, f) Time-history of the log10 residuals aboutthese relationships, with best-fit linear relationships (solid lines). Regression significance is shown by:**(p < 0.01), *(p < 0.05), and n.s. (p > 0.05).

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Unfortunately the survey dates do not coincide with theperiod of river monitoring (1968�2001), thus we estimatedthat the total sedimentation behind the dam during1968�2001 to be �106 m3/yr (or �1.6 Mt/yr assuming abulk density of 1600 kg/m3; Figure 11).[24] Suspended-sediment discharge through Prado Dam

was computed with daily discharge records and the sus-pended-sediment concentrations from the USGS 11074000station (Figure 1). These sediment concentrations did notcorrelate with discharge (r2 = 0.009, n = 448) nor signifi-cantly change with time (best r2 = 0.04, exponentialfunction) even though a wide range of discharge conditionswere sampled. Therefore we used the average concentrationof 490 mg/l (st.dev. = 290 mg/l) for all discharge measure-ments. During the period 1968�2001, total suspended-sediment discharge below Prado Dam was calculated tobe 1.6 ± 1.0 Mt or �0.05 Mt/yr (Figure 11), which is only�3% of the approximated sedimentation behind PradoDam, consistent with the high trap efficiency (>95%)reported by Brownlie and Taylor [1981].

[25] Total flux to the Pacific Ocean was calculated fromthe average annual suspended-sediment discharge past thelower gauging station during 1968�2001 (0.54 Mt/yr) plusan additional 10% bedload transport, an amount recom-mended by Brownlie and Taylor [1981] and Inman andJenkins [1999]. Thus the mass balance (Figure 11) showsthat the majority (�92%; potential range = 81�97%) of thetotal sediment (suspended and bedload) discharged at themouth can be attributed to sediment production in the lowerbasin landscape.[26] Thus, with so little sediment passing through Prado

Dam and with no changes in concentration identified withtime, it is highly unlikely that upper basin sediment dischargeinfluenced the observed shifts in the suspended-sedimentfluxes downstream. Further, although water discharge ratesfrom Prado Dam appear to have changed in a mannerconsistent with those measured downstream, the lowerwatershed produces much more event-based discharge tothe river mouth (twofold to fourfold on average). Theseresults are consistent with the high trap efficiency and floodcontrol procedures of the dam, described above.

5.2. Lower Watershed

[27] We therefore look to the lower watershed forevidence of the changes in water discharge and/or sus-pended-sediment production. The lower watershed mainstem channel shows little evidence for influence, becausethe bed material is much coarser than the suspendedsediment. For example, on average only 2% of the bedmaterial is finer than 0.125 mm (n = 18), while over 75%of the suspended-sediment mass (n = 134) is finer than0.125 mm (USGS 11078000). Thus, although the main stemchannel bed downstream of Prado Dam has been shown todegrade during flood events and aggrade during years withmoderate flow [Brownlie and Taylor, 1981; Nelson, 1982],it cannot be the dominant source of suspended sediment.Further, the bed material grain-size does not show coars-ening or fining trends with time (n = 18; 1967–1987),either of which may suggest alteration of the bed erodibilityand hence sediment production potential.

Figure 10. Comparison of annual peak discharge datafrom the Santa Ana River below Prado Dam (11074000)and at Santa Ana (11078000) during 1968�2001. Doublingscale (2�) is shown with vertical bar. Annual peakdischarge at Santa Ana (SA) is consistently 2�4 timeshigher than at Prado.

Figure 9. Nonlinear, time-dependent relationships ofannual discharge, peak discharge and suspended-sedimentdischarge with respect to precipitation for USGS 11078000.Arrows identify the direction of significant, time-dependentrelationships in (a) power law offset and (b) slope.Significance level is shown by **(p < 0.01), *(p < 0.05)and n.s. (p > 0.05). Best-fit lines are shown at 4-yearintervals.

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[28] The landscape of the lower watershed is therefore thelikely source of change exhibited in the suspended-sedimentrating curve. Here we evaluate two recognized means ofaltering water discharge and sediment production with timewithin southern California: wildfire [Taylor, 1981; Rice,1982; Florsheim et al., 1991] and land use change [Trimble,1997; Pinter and Vestal, 2005].[29] Wildfire has been reported to produce a multiyear

response in landscape erosion and runoff that is greatest inthe immediate year and decays with time. We found thatrunoff, erosion rate and sediment concentration data fromburned areas of semiarid Spain [Cerda, 1998] and the SanGabriel Mountains of southern California [Lave andBurbank, 2004] closely fit exponential decay modelsduring the first 5 years following wildfire (r2 = 0.91 to0.98) and that response half-life (t1/2) ranged between 0.3and 1.2 years. Therefore, to evaluate the effects of the wildfirein the lower watershed, we computed an annual ‘‘effective’’wildfire area using wildfire areas mapped by CaliforniaDepartment of Forestry and Fire Protection (CAFRAP) (Fireperimeters—map, 2004, http://frap.cdf.ca.gov/projects/fire_data/fire_perimeters/, website accessed 7 July 2004) (here-inafter referred to as CAFRAP website) and an exponentialdecay model with variable t1/2 (Figure 12).[30] Annual assessments of land cover were not available,

but decadal inventories show monotonic increases in bothurban land cover and population (Figure 2). This expansionof urban areas was largely at the expense of agriculturallands such as citrus orchards and rangeland (CADC onlinedata). These types of landscape changes have been shown toinduce increases in rainfall-runoff discharge and complexresponses in sediment production [Wolman, 1967; Leopold,

1968; Hollis, 1975; Booth, 1990; Trimble, 1997; Nelson andBooth, 2002]. No significant alteration in grazing practiceswas identified for the Santa Ana River rangeland, whichwould similarly induce sediment production changes [cf.Pinter and Vestal, 2005]. Thus, because better land use datawere not available, we used water year as a proxy for urbanland change effects due to the monotonic increase in urbanland cover with time.[31] Both effective wildfire area and water year provided

significant (p < 0.05) correlations with peak and annualdischarge and annual sediment concentration residualswhen evaluated with stepwise, multiple variable correla-tions (Table 1). Wildfire was shown to significantly increaseannual total and peak discharge, sediment discharge, andsediment concentration. Significant t1/2 were foundbetween 0.4 and 14 years with peak correlations occurringat 1�3 years. An example of the relationship of effectivewildfire area and sediment flux is shown in Figure 13. Alinear model explains roughly 31% of the remainingsediment flux variance (p < 0.01) after the precipitation-relationship, and this model suggests a 10-fold increasebetween no wildfire and a large (200 km2) wildfire.[32] We then reevaluated the scale-dependent temporal

relationships (Figure 9) without the influence of wildfireby correcting the annual time series with the best-fit linearrelationships of effective wildfire area with optimal t1/2.All analyses produced much higher correlation coefficientsthan previous tests without wildfire (Figure 14). Highlysignificant (p < 0.01) scale-dependence changes continue tobe exhibited in total and peak discharge (Figures 14a and14b). The average magnitude of these discharge changeswas sixfold during the 34-year record. Suspended-sedimentdischarge, however, does not exhibit significant changeswith time (Figure 14c), which is counter to the previousscale-dependent analyses (Figure 9c). These results suggestthat: (1) although wildfire significantly increased total and

Figure 11. Total sediment budget for the lower basin ofthe Santa Ana River watershed based on 1968�2001suspended-sediment measurements, estimates of bedloaddischarge, and measurements of Prado sedimentation (seetext). Thickness of the flow diagram is a function of averageannual sediment flux values, which are presented inparentheses. Errors for lower basin inputs are calculatedassuming independent random errors in measurements.

Figure 12. Wildfire history for the lower basin of theSanta Ana River watershed. (a) Annual wildfire area(1950�2003) within the lower watershed from fireboundaries mapped by CAFRAP (website). (b) ‘‘Effective’’burn area computed with an exponential function withvarious half-lives (t1/2, see text).

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peak discharge rates (Table 1), there are very strong tem-poral relationships in discharge irrespective of wildfire(Figures 14a and 14b); and (2) temporal variability ofsediment flux can largely be explained by precipitationand wildfire rather than from a general trend with time,whether scale dependent or independent (Table 1 andFigure 14).

5.3. Rating-Curve Conceptual Model

[33] It was shown above that highly significant temporalchanges were observed in both the suspended-sedimentrating curve and discharge variables of the Santa Ana River.Here we show how these changes are coupled using a ratingcurve conceptual model based on power law formulations,

Css ¼ aQb ð5aÞ

Qss ¼ CssQ ¼ aQ1þb; ð5bÞ

where both suspended-sediment concentration (Css) andflux (Qss) are functions of discharge (Q) based on ratingcurve relationships (a, b). Although we use the power lawformulation here for its mathematical simplicity and generalapplicability to the Santa Ana River, the general principles

Table 1. Multiple-Variable Correlation Matrix for Water Year Variables During the Suspended Sediment Sampling Record (1968�2001)

at USGS 11078000a

Water Year VariableAnnual Precipitation

(log10) Time‘‘Effective’’Wildfire Area

t1/2,years r2

sE(log10)

Suspended-sediment concentration residuals (log10) n.s. �0.036b 0.0015c 0.5–5 0.91 0.15Total annual discharge (log10) 2.87b 0.024b 0.0043b 1.5–10 0.78 0.34Annual peak discharge (log10) 1.27b 0.023b 0.0027b 2–14 0.69 0.24Computed annual sediment flux (log10) 3.69b N.S.d 0.0069b 0.4–12 0.72 0.50

aEach variable was tested with stepwise, linear regression, and the linear slope of significant variables are shown with t-test significance levels (seefootnotes below). The range of each effective wildfire area half-life (t1/2) that was significant (p < 0.05) is also given. The Final two columns present themultivariable regression coefficient (r2) and the standard error of the estimate (sE).

bSignificance level p < 0.01.cSignificance level p < 0.05.dN.S. denotes significance level p > 0.05.

Figure 13. Relationship between effective wildfire burnarea (t1/2 = 2 years) and residual annual suspended-sedimentdischarge. Flux residuals computed as the differencebetween rating curve computations and flux estimated withthe best-fit relationship with precipitation (Figure 8c).Effective wildfire t1/2 = 2 years provided the best linearcorrelation with the residuals.

Figure 14. Identical to Figure 9, except wildfire effectshave been removed by subtracting the best-fit linearrelationship between effective wildfire area and therespective discharge residuals. Single line in Figure 14crepresents nonsignificant (n.s.) temporal relationships (p >0.05).

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presented below are applicable to a broad range of ratingcurve statistical functions [e.g., Hicks et al., 2000; Horowitz,2003].[34] The changes in the Santa Ana River rating curve

resulted largely from decreases in offset (a) with time(Figure 3). Thus we first simplify the conceptual modelby assuming rating curve slope (b) is constant with time,i.e., changes in water and/or sediment discharge exhibitlinear changes in magnitude-frequency relationships. Forthis framework, two periods of time (subscripts 1 and 2)with different water and/or sediment discharge rates can becompared by

rs ¼ rar1þbw ; ð6Þ

where rs is the ratio of sediment flux (Qss1/Qss2), ra is theratio of the sediment rating curve coefficients (a1/a2), and rwis the ratio of water discharge (Q1/Q2). Application of thisconceptual model is provided in Figure 15. Twenty-fold

decreases in sediment rating curves such as exhibited in theSanta Ana River can be produced by either reductions insediment source (Figure 15a) or by increases in waterdischarge (Figure 15b). The latter condition can be under-stood as a dilution-like process, and can occur only if thedischarge increases are independent of sediment production.This dilution process results in a nonlinear relationshipbetween rw and ra (equation (6)). For example, for the meanSanta Ana River b of 0.65, an increase in discharge of onlysixfold will cause a 20-fold reduction in the rating curveoffset (Figure 15b). This simple conceptual model showshow somewhat moderate increases in discharge can causemuch larger decreases in rating curve offset.[35] We next apply this simple conceptual model to the

most significant time-dependent results for the Santa AnaRiver, namely that the discharge increases averaged approx-imately sixfold and were slightly scale dependent, and thesediment flux modifications were related to wildfire(Figure 14). The water discharge modifications would

Figure 15. Conceptual model of sediment rating curve changes induced by sediment source reductionsand water discharge increases. Note that similar results are predicted for very different forcing. Shown arechanges induced by the linear conceptual model (equation (6)) with b equal to 0.65.

Figure 16. Conceptual model of sediment rating curve changes for the Santa Ana River. (a) Inverselyproportional discharge changes with respect to event size (see Figures 14a and 14b). (b) The combinedeffects of Figure 16a and water and sediment flux changes from wildfire, simplified to show only thelargest wildfire, the Paseo Grande of 1967.

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produce a rating curve that shifts as shown above and alsoincreases slightly in slope with time (Figure 16a). Theresulting rating curve change is equivalent to the dominantchanges exhibited in the Santa Ana River (see Figure 3).Wildfire correlated with increases in both water and sedi-ment discharge with a net effect of moderate increasessediment concentrations (a 200 km2 wildfire would doubleconcentrations; Table 1). A simplified representation of howwildfire further modified sediment concentrations is shownin Figure 16b, where the largest wildfire (summer of 1967)is shown to cause a shift up and to the right with moderateeffects on the curve offset. Hence, although wildfire mod-ified watershed fluxes of water and sediment, it does notexplain the large temporal shifts exhibited in the ratingcurve. Thus the conceptual model shows how water dis-charge, rather than sediment flux, produced a time-shiftingrating curve in the Santa Ana River (Figure 16a).

6. Discussion and Conclusions

[36] Large changes in sediment rating curves are typicallyattributed to alterations in river suspended-sediment fluxes,which are in turn related to watershed sediment production[e.g., Van Sickle and Beschta, 1983; Reid and Dunne, 1996;Hovius et al., 2000]. Here we show how hydrologic changescan be major processes in forcing order-of-magnitudealterations in suspended-sediment rating curves, especiallyfor systems with minor suspended-sediment contributionsfrom the river channel. For these conditions, water dis-charge scales nonlinearly with concentration reductions,and the power law slope of this relationship, 1 + b(equation (6)), will commonly range between 1.5 and 3[cf. Syvitski et al., 2000]. For these conditions, many-foldalterations in discharge will produce order-of-magnitudechanges in concentration.[37] Addition of dilute water to a channel is a neces-

sary condition for the proposed dilution model, but it isnot sufficient to cause reduced suspended-sediment con-centrations or to maintain a constant long-term sedimentflux. If sediment were available locally in the channel,inputs of dilute water could be expected to erode andsuspend sediment, thereby increasing concentrations backto past levels (if channel sediment and geometryremained constant). As shown above, however, the mainstem channel of the Santa Ana River effectively behavedas a pipe rather than an alluvial channel with respect tothe suspended-sediment.[38] Large changes in precipitation-discharge relation-

ships are first-order characteristics of hydrologic responsesto urbanization [e.g., Leopold, 1968; Gregory, 1974; Hollis,1975]. As noted by hydrologic analyses of White and Greer[2006], urbanization in southern California of the same scale(from 10% to 40% urbanized) induced order-of-magnitudeincreases in the low-magnitude (1- to 2-year recurrence)peak and annual discharges and more moderate to negli-gible increases for the largest (>10-year recurrence) events,which is consistent with the data presented here (Figures 14aand 14b) and within other southern California watersheds[e.g., Trimble, 1997]. Although the Santa Ana River dis-charge rates were surely influenced by the upper basin, thesecontributions were secondary compared to the dischargegenerated in the lower basin. Stated simply, Santa Ana River

discharge increased in a manner coherent and consistent withother urbanizing southern California watersheds. We there-fore suggest an urban hydrologic response for the Santa AnaRiver during the period considered.[39] Once the effects of wildfire were removed, no time-

dependent relationship was found between sediment dis-charge and time (Figure 14 and Table 1). This suggests thatthe land use changes with time had little effect on the totalsediment flux from the basin. Urbanization has been notedto alter rates of sediment production, although this sedimentproduction response may be complex owing to increasesand/or decreases in landscape erosion and channel scourand/or armoring, all which may be related to the hydrologicchanges of the basin [Keller, 1962; Wolman, 1967; Wolmanand Schick, 1967; Booth, 1990; Trimble, 1997]. We hy-pothesize that the steady rate of sediment discharge during atime of urbanization could have been a result of: (1) contin-ual disturbance by the relatively constant land use conver-sion, or (2) sediment production dominance in the ruraluplands above the urban regions.[40] Wildfire effects were evident in water discharge,

sediment flux and sediment concentrations, which is con-sistent with other semi-arid regions [Los Angeles CountyFlood Control District, 1959; Taylor, 1981; Rice, 1982;Florsheim et al., 1991; Cerda, 1998; Moody and Martin,2001; Lave and Burbank, 2004]. Although wildfire wasshown to significantly correlate with both water and sedi-ment discharge, the net effect was an increase in suspended-sediment concentrations (Table 1 and Figure 16). Thissuggests that the relative increase of sediment productionwas greater than that of discharge, consistent with theresults of Cerda [1998]. Wildfire effects also fit exponentdecay models with peak correlations occurring with t1/2 of1�3 years. These values were somewhat larger than thosecomputed from other research (0.3�1.2 years, see above),which supports the hypothesis of Lave and Burbank [2004]that larger watersheds (such as the Santa Ana River) wouldexhibit a longer time delay compared to the landscape andfirst-order drainage basins cited in the wildfire literature.The 1967 Paseo Grande fire, which was the largest wildfireon record (Figure 12a), was responsible for elevated dis-charge and sediment production during the beginning of the1968�2001 sampling record, including the year of largestdischarge, 1969.[41] If modifications to the Santa Ana River are repre-

sentative of changes in other southern California rivers,most of which have urbanized at similar rates [cf. White andGreer, 2006], we estimate that present-day loads would beoverpredicted by an order-of-magnitude owing to the effectsof increases in discharge (Figures 14a and 14b) andoutdated rating curves. This is especially important becauseriver sampling has been dramatically reduced or eliminatedon most coastal rivers during the past two decades whenmassive development and population growth has occurred.Although extending rating curves beyond the samplinghistory is generally not accepted [Porterfield, 1972], wenote that sediment flux inventories for southern Californiause such techniques owing to data limitations [Brownlie andTaylor, 1981; Inman and Jenkins, 1999; Willis and Griggs,2003]. Thus inventories of southern California coastallittoral and margin-wide sediment budgets, which are dom-inated by river suspended-sediment fluxes [Inman and

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Jenkins, 1999; Schwalbach and Gorsline, 1985], may besubstantially overestimated.[42] This pattern of landscape modification coupled with

reduced sampling of rivers is not limited to the southernCalifornia region, but is endemic of watersheds globally aspointed out by Vorosmarty et al. [2001], Shiklomanov et al.[2002] and Beach [2002]. We suggest that reinvigoratedsampling efforts will be needed not only to characterize landuse impacts such as described here and by Vorosmarty et al.[2004] and Syvitski et al. [2005], but also to evaluate thehydrologic effects of future climate change, which may begreat [Inman and Jenkins, 1999; Vorosmarty et al., 2000;Peterson et al., 2002].[43] Thus the 34-year sampling record examined here was

extremely valuable for identifying not only the magnitudeof suspended-sediment concentration changes but also thelandscape causes of these changes. We emphasize that landuse and landscape changes can alter both sediment fluxesand water discharge in rivers, both of which can have largeeffects in altering suspended-sediment concentration rela-tionships. Without careful consideration of these effects,order-of-magnitude errors can be made in flux calculations.

Appendix A: Evaluation of Sampling Techniqueand Timing

[44] We evaluated the possibility that the changes ob-served in the suspended-sediment data were not caused bygeomorphic or hydrologic process, but rather were anartifact of a change in sampling technique or timing.However, the sampling technique of flow-weighted,depth-integrated sampling was not altered during the record.Such a change would likely produce a step-function in theresiduals with respect to time, rather than the gradualchange observed (Figure 4b).[45] There did appear to be a change in the timing of the

sample collection with time, however. For example, ifsamples were split into two equal-length, sequential groups,the latter group had 26% less samples on days of peakdischarge (Figure A1a). The latter period made up for thisdeficit with samples both on days prior to and followingpeak discharge. This suggests that although sampling hasconsistently focused on event discharge, sampling was lesslikely to sample on a day of peak discharge in the latterportion of the record.[46] This change in sampling timing could influence

temporal patterns in the rating curve if there were signifi-cantly lower concentrations measured on the nonpeakdischarge days. However, very little difference was ob-served in the sediment concentration residuals (actual minusbest-fit power law curve in Figure 4) for the different daysof sampling (Figure A1b). Box plots of these groupings hadsubstantial overlap, and t-test comparisons of the residualssuggested that the mean values of most groups were notsignificantly different (p < 0.05). The only significantlydifferent groups (p < 0.05) were the samples obtained5+ days following peak discharge (mean residual =�0.44), which were lower than the samples obtained onthe day before peak (mean residual = 0.08; p = 0.04) and theday of peak discharge (mean residual = 0.10; p = 0.015). Ifthe mean residuals (Figure A1b) were weighted by the

sampling histograms (Figure A1a), however, total differencein the two sampling periods was only 0.056 log10 units,equivalent to a change by a factor of 1.14. This is equivalentto a �30% reduction during 1968�2001 if continuous(equivalent to 1.142), considerably less than the �2000%average change observed.[47] Last, the results above (Figure A1b) suggest that

consistent event hysteresis patterns may not exist. This issupported by hydrologic events with multiple samples(Figure A2). Of the 7 events with multiple samples, 2 showclockwise, 4 show counterclockwise and one shows nodistinguishable hysteresis (Figure A2). Thus no consistentevent hysteresis was identified. Further, an analysis ofseasonal effects on sediment concentrations reveals thatconcentration residuals were not significantly different fromzero during the months with the majority of sampling(Figure A3).

Figure A1. Evaluation of sample timing on suspended-sediment concentrations for the Santa Ana River at SantaAna (USGS 11078000). (a) Histogram of the timing ofsuspended sediment sampling. Data have been separatedinto six groups based on number of days since a peakdischarge (zero defined to be the day of peak discharge).The first half of the samples (1�103) were obtained fromNovember 1967 to January 1980, the second half(104�206) from January 1980 to March 2001. (b) Relation-ship between timing of suspended-sediment sample andsuspended-sediment concentration. Residuals are based onthe logarithmic difference between concentration and best-fit power regression from Figure 3. Box plots are defined bythe quartiles, and the whiskers are the minimum andmaximum values if within 1.5 times the interquartiledistance. Points are outliners of these whiskers, and plusesare mean values.

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Figure A2. Event rating curves to evaluate hysteresis for the Santa Ana River at Santa Ana (USGS11078000). Direction of hysteresis is labeled on each plot as clockwise (CW), counterclockwise (CCW),or neither (none). Each plot is labeled with the date of peak discharge and includes the best-fit powerrelationship through all data (dashed line). No consistent hysteresis pattern is observed in these data.

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[48] Acknowledgments. Basil Gomez, Michael Church, and an anon-ymous reviewer significantly improved this paper with their comments.Tony Orme, Derek Booth, and Noah Snyder contributed detailed reviews ofan earlier draft of the manuscript, for which we are very grateful. We alsothank John Milliman, Noah Snyder, Jodi Harney, and Eric Grossman forinsightful discussions early in our investigations. G. I. Bergquist atCalifornia D.W.R. supplied land use data and Kevin Orzech, Lori Hibbeler,Beth Feingold, and Florence Wong assisted with data management andanalysis. Greg Peacock at the Los Angeles District of USACE assisted withhistorical information on Prado Dam and the Santa Ana River channel. J. A.W. was supported by a USGS Mendenhall Postdoctoral Fellowship and aNASA Oceans and Ice Research Project Award (NRA-04-OES-02).

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�����������������������D. M. Rubin and J. A. Warrick, USGS Coastal and Marine Geology

Program, U.S. Geological Survey, 400 Natural Bridges Drive, Santa Cruz,CA 95060, USA. (jwarrick@usgs.gov)

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